Details

Time bar (total: 1.5m)

sample152.0ms

Algorithm
intervals
Results
42.0ms234×body80nan
39.0ms99×body160valid
29.0ms157×body80valid

simplify403.0ms

Calls
1 calls:
Slowest
403.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize36.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.6b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.4b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt
71×times-frac
58×*-un-lft-identity
51×add-cube-cbrt
21×sqrt-prod
18×add-cbrt-cube add-exp-log
14×difference-of-squares
13×swap-sqr associate-*r* associate-*l*
12×pow1
6×div-inv
5×cbrt-undiv div-exp associate-/l*
4×prod-exp associate-/r/ cbrt-unprod insert-posit16 add-log-exp unswap-sqr
3×associate-/r*
2×rem-sqrt-square flip3-+ flip-+ associate-/l/
1×pow2 frac-times asin-acos clear-num frac-2neg sqrt-pow1 pow-plus flip3-- pow1/2 sqrt-div div-sub pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Calls
4 calls:
Slowest
30.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
18.0ms
(* (/ Om Omc) (/ Om Omc))
13.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series393.0ms

Calls
4 calls:
Slowest
197.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
132.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
44.0ms
(* (/ Om Omc) (/ Om Omc))
21.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify16.2s

Calls
156 calls:
Slowest
572.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
510.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
426.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
354.0ms
(- 1 (* 2 (* (/ t l) (/ t l))))
293.0ms
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

prune2.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 11.7b

localize30.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
0.6b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))
0.4b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))
0.3b
(/ 2 (* (/ l t) (/ l t)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
44×times-frac
39×add-sqr-sqrt
27×add-cube-cbrt
26×sqrt-prod
24×add-cbrt-cube add-exp-log
18×difference-of-squares
11×distribute-lft-out
10×cbrt-undiv div-exp
8×associate-/l*
7×associate-/r/
5×pow1 associate-/r*
4×prod-exp cbrt-unprod insert-posit16 add-log-exp
3×div-inv
2×rem-sqrt-square clear-num frac-2neg flip3-+ flip-+ associate-/l/
1×frac-times asin-acos sqrt-pow1 flip3-- pow1/2 sqrt-div div-sub associate-*l/ associate-*r/ flip--
Calls
4 calls:
Slowest
58.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))
36.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
10.0ms
(/ 2 (* (/ l t) (/ l t)))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))

series348.0ms

Calls
4 calls:
Slowest
169.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
92.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))
67.0ms
(/ 2 (* (/ l t) (/ l t)))
19.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))

simplify17.5s

Calls
117 calls:
Slowest
724.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))
509.0ms
(+ (* (/ 2 (* (/ l t) (/ l t))) (/ 2 (* (/ l t) (/ l t)))) (- (* 1 1) (* (/ 2 (* (/ l t) (/ l t))) 1)))
421.0ms
(/ (* (* 2 2) 2) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))
407.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ (/ 2 (* (/ l t) (/ l t))) 1)))
392.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))

prune2.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 11.7b

localize39.0ms

Local error

Found 4 expressions with local error:

10.8b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.6b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.4b
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
88×times-frac
85×add-sqr-sqrt
72×*-un-lft-identity
65×add-cube-cbrt sqrt-prod
18×add-cbrt-cube add-exp-log
14×difference-of-squares
13×swap-sqr associate-*r* associate-*l*
12×pow1
8×associate-/l*
6×associate-/r* sqrt-div
5×cbrt-undiv div-exp div-inv
4×prod-exp cbrt-unprod insert-posit16 add-log-exp unswap-sqr
2×flip3-+ associate-/r/ flip-+ associate-/l/
1×pow2 frac-times rem-sqrt-square asin-acos sqrt-undiv clear-num frac-2neg sqrt-pow1 pow-plus flip3-- pow1/2 pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Calls
4 calls:
Slowest
25.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
25.0ms
(* (/ Om Omc) (/ Om Omc))
5.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
2.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series295.0ms

Calls
4 calls:
Slowest
147.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
108.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
29.0ms
(* (/ Om Omc) (/ Om Omc))
11.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify26.6s

Calls
210 calls:
Slowest
484.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
479.0ms
(sqrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))
431.0ms
(/ (* (* (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (* (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
392.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
300.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))

prune2.9s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 6.3b

localize47.0ms

Local error

Found 4 expressions with local error:

11.1b
(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
11.1b
(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
10.6b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
10.6b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
48×sqrt-prod
38×add-sqr-sqrt
32×times-frac
30×*-un-lft-identity
24×add-cube-cbrt
12×difference-of-squares
8×pow1
6×rem-sqrt-square
4×sqrt-pow1 add-cbrt-cube pow1/2 add-exp-log associate-/r/ insert-posit16 add-log-exp
2×flip3-+ sqrt-div flip-+ div-inv
Calls
4 calls:
Slowest
15.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
15.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
2.0ms
(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
2.0ms
(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))

series437.0ms

Calls
4 calls:
Slowest
183.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
168.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
55.0ms
(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
31.0ms
(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))

simplify12.6s

Calls
72 calls:
Slowest
687.0ms
(sqrt (* (cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))) (cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))))
337.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
323.0ms
(sqrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
320.0ms
(sqrt (asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1)))))
320.0ms
(sqrt (sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))))

prune1.9s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.3b

regimes725.0ms

Accuracy

98.3% (0.1b remaining)

Error of 5.5b against oracle of 5.5b and baseline of 10.3b

bsearch17.0ms

end0.0ms

sample4.9s

Algorithm
intervals
Results
2.0s7695×body80nan
1.6s3717×body160valid
839.0ms4283×body80valid